Lithography and, in particular, photolithography is a well-known technique in semi-conductor and printed circuit board (PCB) manufacture for creating electrical components and circuits. Photolithography involves placing a mask in front of a substrate, which has been covered by a layer of photoresist, before exposing to light. The areas of photoresist exposed to the light react and change chemical properties compared with the unexposed photoresist. The photoresist is then developed for removing either the exposed portions of photoresist for a positive resist or unexposed portions for a negative resist. The pattern formed in the photoresist allows further process steps to be performed on the substrate, such as, but not limited to, etching, deposition or implantation.
The resolution of photolithography is limited by the diffraction of light from the mask features. As the separation between the mask and the substrate increases, so the minimum feature size increases, thus fine-line photolithographic methods are only suitable for flat surfaces. Photolithography on non-planar surfaces has been achieved by moulding the mask to the shape of the substrate prior to exposing. This specialised technique is only suitable for large simple shapes.
Holographic masks have been constructed using a traditional Total Internal Reflection (TIR) holographic technique to pattern sub-micron features onto large (for example, 15×15 inch) flat substrates. The holographic mask is much more robust to defects than a standard mask and does not need to be in intimate contact with the substrate in order to generate high definition features. Techniques have also been devised for projecting a pair of TIR holographic masks onto a spherical substrate. The technique involves a complicated optical set-up to generate the holograms.
Systems for creating Computer Generated Holograms (CGHs), mainly for use in holographic displays, have also been devised. CGHs are created by defining an object or shape geometrically inside a computer and computing the required patterning of a diffraction mask. A holographic image of that object is created when a suitable light source is emitted towards the diffraction mask.
A CGH system designs the holographic interference pattern which is plotted or printed. A hologram is generated when the pattern is exposed to a monochromatic light source. In common use, and in this context, CGH describes the whole process of creating a hologram from generation of interference pattern within a computer to exposure of the pattern to a light source.
Conventionally, CGH patterns for the projection of a light distribution into a 3D volume have been calculated in a number of ways including:    1. split the volume into a number of slices and compute the Fresnel Diffraction Formula (FDF) for each slice;    2. split the volume into a number of planar segments at various inclinations to the hologram plane and superimpose the results of the FDF for each planar segment; and    3. decompose the object within the volume into line segments and superimpose the results of the FDF for each line segment.
The first method requires an optical calculation for every slice through the object volume, each comprising a two-dimensional Fourier Transform and multiplicative factors. Similarly, the second method requires calculation of a two-dimensional Fourier Transform, multiplication by exponential phase factors and a coordinate transform for each plane into which the object has been split. Calculation of diffraction patterns using these methods for large or high-resolution diffraction masks is computationally expensive.
Calculations based on the third method are more efficient, because the pattern in the hologram plane can be calculated analytically. This is demonstrated in “Computer-generated holograms of three-dimensional objects composed of line segments” Ch. Frére, D. Lesenberg, O. Bryngdahl, J Optical Society of America 3 (1986) 726-730, where the technique is used in relation to generating a holographic display. Unfortunately, this method does not provide adequate means for precisely controlling line width and length and therefore cannot be used for precise applications.